Questions: Lashonda wants to save money to open a tutoring center. She buys an annuity with a yearly payment of 489 that pays 3% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 7 years. Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. [I]

Solution Steps

To find the total value of the annuity in 7 years, we can use the future value of an ordinary annuity formula: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where:

• $P$ is the yearly payment (\$489),
• $r$ is the annual interest rate (3% or 0.03),
• $n$ is the number of years (7).

We are given:

• Yearly payment $P = 489$
• Annual interest rate $r = 0.03$
• Number of years $n = 7$

The future value $FV$ of an ordinary annuity can be calculated using the formula: $$FV = P \times \frac{(1 + r)^n - 1}{r}$$

Substitute $P = 489$, $r = 0.03$, and $n = 7$ into the formula: $$FV = 489 \times \frac{(1 + 0.03)^7 - 1}{0.03}$$

First, calculate $(1 + 0.03)^7$: $$(1 + 0.03)^7 = 1.03^7 \approx 1.225043$$

Next, calculate $1.225043 - 1$: $$1.225043 - 1 = 0.225043$$

Then, divide by the interest rate $0.03$: $$\frac{0.225043}{0.03} \approx 7.501433$$

Finally, multiply by the yearly payment $489$: $$489 \times 7.501433 \approx 3669.199$$

Round the final value to the nearest cent: $$3669.199 \approx 3669.20$$

Final Answer